Find a symoblic expression for the emf induced in the coil in terms of the varia

Question

Find a symoblic expression for the emf induced in the coil in terms of the variables?

if each loop has resistance R, find an expression for the magnitude of the induced current?

An N-turn circular wire coil of radius r lies in the xy-plane, as shown in the figure below. A uniform magnetic field is turned on, increasing steadily from 0 to 80 in the negative z-direction in t seconds. (Use any variable or symbol stated above along with the following as necessary: R and pi.) Find a symbolic expression for the emf, , induced in the coil in terms of the variables given. Looking down at the xy-plane from the positive z-axis, is the direction of the induced current clockwise or counterclockwise? If each loop has resistance R, find an expression for the magnitude of the induced current, I.

Explanation / Answer

a. this is obtanied from Faradays law of EM induction.

this staes that the net amount amount o induced emf generated across a conductor is directly proportional to thne rate at which magnetic flux changes

i.e let induced emf be e,

then e = -d(phiB)/dt

-ve sign appears because of lenz law,

A = area = pi r^2 for circular cross section

for N no. of turns

e = -N A dB0/dt

e = N(pi R^2) B0/t

b. counter clock wise

c. induced current i = induced emf/resistance

i = e/R = -(NAdB0/dt)/R

i =N(pi R^2) B0/Rt

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